A triangle has sides with lengths of 2x - 7, 5x - 3, and 2x

What is the sum of the geometric sequence −4, 24, −144, ... if there are 8 terms?

Helga [31]

Answer:

The sum of 8 geometric sequence is 959780

Step-by-step explanation:

We are given

this sequence is geometric

-4 , 24 , -144

First term is -4

so, $a_1=-4$

now, we can find common ratio

$r=\frac{24}{-4}=-6$

we can use formula

$S_n=a_1(\frac{1-r^n}{1-r} )$

n=8

now, we can plug values

$S_8=-4(\frac{1-(-6)^{8}}{1+6} )$

now, we can simplify it

and we get

$S_8=959780$

4 0

4 years ago

Write a set of data with six values that has a mean of 28, median of 29, and a range of 18

Basile [38]

Mean is average example
mean of x,y,z is (x+y+z)/3

so 6 values
mean of 28
that means that they add up to 168

median means the middle number when you arrange them
range means the distance from smallest number to largest number

an example

18,27,29,29,29,36

4 0

3 years ago

In one year the perseid metor shower had a metor appear every 1/5 5 minutes on average That same year the Leonid metor shower ha

olga55 [171]

In one year, the Perseid meteor shower had a meteor appear every 1 1/5 minutes on average. That same year, the Leonid meteor shower had a meteor appear every 4 2/3 minutes on average. How many more meteors fell during the Perseid meteor shower?

Answer:

325,452 meteors

Step-by-step explanation:

We all know that :

We have 365 days in a year and in each day there are 24 hours, Likewise an hour has 60 minutes

SO, the total number of minutes in a year is :

365 × 24 × 60 = 525600 minutes

For Perseid meteor:

$1 + \frac{1}{5} \\ \\ = 1 + 0.2 \\ \\ = 1.2$

So one meteor fall at 1.2 minutes interval Thus, in a year, we will have :

1 meteor - 1.2 minutes.

x meteor - 525600 minutes.

1.2x = 525600

$x = \frac{525600}{1.2}$

x = 438000

∴ 438,000 meteors fell during the Perseid shower.

For Leonid meteor shower:

$4 + \frac{2}{3} = 4.67$

So one meteor fall at 4.67 minutes interval Thus, in a year, we will have :

1 meteor - 4.67 minutes.

x meteors - 525600 minutes.

$4.67x = 525600$

$x = \frac{525600}{4.67}$

x = 112548

112,548 meteors fell during the Leonid Shower.

Finally , the numbers of more meteors that fell during the Perseid meteor shower is calculated by the difference in the number of Perseid meteor shower and Lenoid meteor shower. i.e

438,000 - 112,548 = 325,452

325,452 more meteors fell during the Perseid meteor shower

5 0

3 years ago

Assume that x equals x (t )and y equals y (t ). Let y equals x cubed plus 4 and StartFraction dx Over dt EndFraction =2 when xe

nika2105 [10]

Answer:dy/dt(x=3)=54

Step-by-step explanation:

We know that we can write:

$\frac{dy}{dt}=\frac{dy}{dx} *\frac{dx}{dt}$

and so evaluate it as a product of functions, that is for a given value of x or t, we get that

$\frac{dy}{dt}(s)=\frac{dy}{dx} (s) * \frac{dx}{dt}(s)$ .

Now we are told that:

$1. x=x(t),\ 2.y=x^3+4,\ \frac{dx}{dt} =2,\ for \ x=3,$

whenever it happens, this means the influence of t is hidden, and we only consider the result, that is, how much is x when the derivative has the value of 2, we are not concerned for what value of t it happens, since we get all the necessary information beforehand.

Now we need to calculate

$\frac{dy}{dx}=3x^2 \rightarrow \frac{dy}{dx}(3)=3(3)^2=27$ .

Therefore

$\frac{dy}{dt}(x=3)=\frac{dy}{dx} (x=3) * \frac{dx}{dt}(x=3)$ or

$\frac{dy}{dt}(x=3)=27 *2 = 54$ .

7 0

4 years ago

A study found that 1% of Social Security recipients are too young to vote. If 800 social security recipients are randomly select

GalinKa [24]

Answer:

8, 7.92, 2.81

Step-by-step explanation:

For each Social Security recipient, there are only two possible outcomes. Either they are too young to vote, or they are not. The probability of a Social Security recipient is independent of any other Social Security recipient. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$